function PDE = process_pde_2d(exmple_index)
switch exmple_index
    case 1
        a = 1;
        b = 2;
        PDE.lambda = a;
        PDE.mu = b;
        PDE.index = exmple_index;
        PDE.u1 = @(x,y) sin(pi*x).*sin(pi*y);
        PDE.u1dx = @(x,y) pi*cos(pi*x).*sin(pi*y);
        PDE.u1dy = @(x,y) pi*cos(pi*y).*sin(pi*x);
        PDE.u2 = @(x,y) x.*(x-1).*y.*(y-1);
        PDE.u2dx = @(x,y) y.*(2*x - 1).*(y - 1);
        PDE.u2dy = @(x,y) x.*(2*y - 1).*(x - 1);
        PDE.f1 = @(x,y) -(a+2*b)*(-pi^2*sin(pi*x).*sin(pi*y)) - (a+b)*((2*x-1).*(2*y-1)) - b*(-pi^2*sin(pi*x).*sin(pi*y));
        PDE.f2 = @(x,y) -(a+2*b)*(2*x.*(x-1)) - (a+b)*(pi^2*cos(pi*x).*cos(pi*y)) - b*(2*y.*(y-1));
        PDE.domain = [0, 1, 0, 1];
        PDE.bdary = [0, 0, 0, 0];
    otherwise
        error("Invalid PDE exmple_index");
end
fprintf("PDE example: %d (有解析解的问题)\n", exmple_index);
fprintf("PDE domain: xmin,xmax,ymin,ymax\n");
disp(PDE.domain);
fprintf("PDE boundary: bottom,right,top,left (0=Dirichlet,1=Neumann,2=Robin)\n");
disp(PDE.bdary);
end